EXCHANGE 


UNIVERSITY  OF /PENNSYLVANIA 


22 


THE  THERMODYNAMIC  PROPERTIES 

OF  SOLUTIONS  OF  ONE-TENTH  MOLAL 

HYDROCHLORIC  ACID,  CONTAINING 

CALCIUM,  STRONTIUM  AND 

BARIUM  CHLORIDES 


BY 

NORMAN  JODON  BRUMBAUGH 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  IN 

PARTIAL   FULFILLMENT    OF    THE   REQUIREMENTS   FOR 

THE   DEGREE   OF   DOCTOR  OF  PHILOSOPHY 

IN    CHEMISTRY 


MARTIN  &  LYLE,  PRINTERS 

212  PENFIELD  BUILDING 

PHILADELPHIA 

1922 


UNIVERSITY  OF  PENNSYLVANIA 


THE  THERMODYNAMIC  PROPERTIES 

OF  SOLUTIONS  OF  ONE-TENTH  MOLAL 

HYDROCHLORIC  ACID,  CONTAINING 

CALCIUM,  STRONTIUM  AND 

BARIUM  CHLORIDES 


BY 

NORMAN  JODON  BRUMBAUGH 
n 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  IN 

PARTIAL   FULFILLMENT    OF    THE    REQUIREMENTS    FOR 

THE   DEGREE   OF   DOCTOR  OF  PHILOSOPHY 

IN    CHEMISTRY 


MARTIN  &  LYLE,  PRINTERS 

212  PENFIELD  BUILDING 

PHILADELPHIA 

1922 


The  author  desires  to  express  his  appreciation  to  Dr. 

Herbert  S.  Harued,  who  suggested  the  general 

plan  of  this  investigation  and  from  whom 

valuable  assistance   and  direction 

were  frequently  received. 


; 


THE    THERMODYNAMIC    PROPERTIES    OF    SOLUTIONS    OP    0.1 

MOLAL  HYDROCHLORIC  ACID  CONTAINING  CALCIUM, 

STRONTIUM  AND  BARIUM  CHLORIDES. 


In  several  recent  contributions,  Harned  (Jour.  Amer.  Chem.  Soc.  37, 
2460  (1915)  ;  38,  1986  (1916)  •  43,  1808  (1920)  from  measurements  of  cells 
of  the  type 

H2|MeCl  (c)  in  HC1  (0.1)|  HgCl  |Hg 
and  H2|MeCl  (c)  in  HC1  (0.1)|Sat.KCl|HgCl|Hg 

where  Me  represents  potassium,  sodium,  or  lithium,  has  attempted  to  com- 
pute the  independent  hydrogen  and  chlorine  ion  activities  of  these 
solutions.  In  all  these  cells  the  concentration  of  the  acid  has  been  kept 
constant  and  the  salt  varied.  Loomis,  Essex  and  Meacham  (Jour.  Amer. 
Chem.  Soc.  39,  1133  (1917)  and  Ming  Chow  (ibid.  42,488  (1920),  have 
also  measured  cells  of  the  same  type  containing  hydrochloric  acid  and 
potassium  chloride,  but  in  their  measurements  the  total  chlorine  ion  con- 
centration was  kept  constant. 

In  the  present  investigation  accurate  measurements  of  the  same  types 
of  cells  have  been  made,  employing  barium,  strontium  and  calcium 
chlorides  in  0.1  M  hydrochloric  acid.  The  exact  calculation  of  the  in- 
dividual activity  coefficients  of  the  ions  in  concentrated  solutions  is  a 
problem  accompanied  with  great  difficulties  owing  to  liquid  junction 
potentials  which  cannot  be  accurately  calculated.  At  the  present  time, 
the  only  other  method  of  value,  besides  calculations  which  are  inexact,  is 
to  eliminate  as  far  as  possible  the  liquid  junction  potential  by  the  use  of  a 
saturated  potassium  chloride  solution.  From  previous  results  obtained  by 
Harned  (loc.  cit.)  there  is  considerable  evidence  that  the  difference  in 
liquid  junction  potential  between 

HC1  (O.l)jSat.  KC1 
and  HC1  (0.1)  +MeCl      |Sat.  KC1 

if  present  at  all,  is  very  small,  probably  amounting  to  less  than  a  millivolt 
when  the  MeCl  is  as  concentrated  as  2M.  Although  this  error  due  to 
liquid  junction  is  appreciable,  and  the  calculations  cannot  be  regarded  as 
exact,  it  is  thought  that  further  experimental  work  of  this  nature  is  of 
very  great  value,  particularly  since  no  other  method  has  yet  been  found 
which  can  approach  it  in  accuracy. 


'4  *  '    TMRMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCh,  SrCb  AND  BaCb 

1.    GENERAL  THEORY. 

If  a  process  is  carried  out  reversibly,  the  maximum  work  is  inde- 
pendent of  the  path.  Hence,  if  the  system  passes  from  a  state  I  to  a  state 
II,  the  maximum  work  may  be  regarded  as  the  difference  in  two  quantities 

AI  and  A2.     Thus, 

Maximum  work  =  AI  —  A2  =  —  (A2  —  AI)  =  (  —  A  A) 
Now,  take  for  example,  the  voltaic  cell 

ZnlZn**  ||H+|H2 
and  let  the  process 

Zn+2H+  =  ZnVH2 

take  place  reversibly  at  constant  pressure  producing  the  electrical  work 
W.  W  is  not  the  quantity  (-AA)  for  besides  W  there  will  be  the  work 
PAV  done  by  the  production  of  1  mol.  of  hydrogen.  Hence, 

W=(-AA)-PAV  (1) 

Let        F=A+2pV 

and    AF  =  AA+2pAV  (2) 

AP  will  be  the  increase  in  free  energy  of  the  system.  In  the  above 
cell  let  nEF  be  the  electrical  work.  Then,  the  total  maximum  work  will 
be  (-  A  A)  and 

(-AA)=nEF+PAV  (3) 

or  from  (2)  and  (3) 

nEF=(-AA)-pAV=(-AF)* 
*(See  Lewis  —  Jour.  Amer.  Chem.  Soc.  35,  1  (1913) 

Thus,  the  electrical  work  at  constant  pressure  and  temperature  of  a 
reversible  cell  is  equal  to  the  free  energy  decrease.  In  order  to  calculate 
AH,  the  increase  in  heat  content  function,  from  measurements  of  AF, 
use  will  be  made  of  the  fundamental  thermodynamic  formula 


AH=AF-Td  (4) 

The  activity  can  be  defined  by  the  equation 

F=RTlna+i  (5) 

where  F  is  the  partial  molal  free  energy,  i  a  constant,  R  the  gas  constant 
and  T  the  absolute  temperature. 

Thus,  the  free  energies  of  an  ion  species  in  two  states  are  related  by 

AF  =  F2-F1  =  RTln-  (6) 

ai 

(6)  will  be  the  exact  formula  for  the  free  energy  change  of  a  con- 
centration cell.    Consider  the  general  reaction 

aA-f-bB+..      .  .=dD+eE.. 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  OaCb,  SrCb  AND  BaCL       5 

Let  it  take  place  electrically.     Then  it  is  easily  proved  (Lewis — loc. 
cit.)  that 


(-AF)  =  nEF  =  -RTln        -  (7) 

aA      aB 

Two  types  of  cells  will  be  considered  in  the  present  investigation  : 
Type  I      H2  |  MeCl2  (c)  in  HC1  (0.1)  |    HgCl    |  Hg 
Type  II     H2  |  MeCl2  (c)  in  HC1  (0.1)  |  Sat.KCl  |  HgCl  |  Hg 
The  electromotive  forces  of  the  above  cells  will  be  denoted  by  E(l),  and 
E(2)  respectively.     Also  let  E0(l)  equal  E(l)  when  c  =  o;  E0(2)  equal  E(2) 
when  c  =  o. 

2  E(1)F  will  be  the  free  energy  decrease  (  —  AF)  of  the  cell  reaction. 

H2+2  HgCl  =  2  Hg-f  2  HC1  (c) 

in  the  presence  of  HC1  (0.1M)  and  the  acid-salt  mixtures.    Then 

F[E0(1)-E  (l)]  =  (- 

.  . 

where     (_AF)jis  the  decrease  in  free  energy  of  transfer  of  two  mols  of 

hydrochloric  acid  from  (MeCl2  (c)  +  HC1  (0.1)  to  HC1  (0.1).    (aH(s))  refers 
to  the  activity  of  the  hydrogen  ion  in  the  acid-salt  mixtures.) 


Further  F[E0(2)-E(2)]  =  (-AF)2  =  RT  In  -- 

aH(0.1) 

if,  in  the  latter  case,  the  potassium  chloride  solution  eliminates  the  liquid 
junction  difficulties. 

A  further  quantity  which  is  often  used  is  the  activity   coefficient 

which  for  a  single  ion  is  defined  by_  where  c  is  the  molal  concentration  of 
the  ion.  c 

2.  EXPERIMENTAL. 
a.  Materials. 

The  various  chemicals  used  in  making  the  cells  were  carefully  tested 
as  to  their  purity  and  most  of  the  materials  were  prepared  for  this  par- 
ticular investigation  from  analyzed  chemicals.  The  aim  sought  was  to 
avoid  error  in  the  electromotive  force  measurements  from  possible  con- 
taminating impurities  in  the  stock  materials. 

The  mercury  used  was  distilled  three  times  under  reduced  pressure. 
During  the  distillation  a  stream  of  air  was  passed  through  the  mercury 
in  the  flask  in  order  that  all  traces  of  zinc  and  cadmium  might  be  oxidized 
and  thereby  separated  from  the  vaporized  mercury.  This  purified  mer- 
cury was  used  in  the  calomel  electrode  chamber  of  all  the  cells.  Also  a 


6        THERMODYNAMIC  PEOPEETIES  OF  0.1  M  HC1  IN  CaCb,  SrCk  AND  Bad* 

portion  of  it  was  treated  with  a  limited  amount  of  nitric  acid  which  had 
been  previously  redistilled  over  solid  potassium  permanganate.  From  a 
boiling  solution  of  the  mercurous  nitrate  thus  formed,  the  calomel  for  the 
cells  was  precipitated  by  the  addition  of  redistilled  hydrochloric  acid.  The 
precipitated  calomel  was  washed  until  all  traces  of  hydrochloric  acid  had 
disappeared,  about  forty  times.  The  last  two  or  three  washings  were  made 
with  redistilled  water. 

All  water  used  in  making  up  solutions  of  the  electrolytes  had  been 
redistilled  from  an  alkaline  potassium  permanganate  solution  through  a 
block  tin  condenser. 

The  barium  chloride  was  prepared  from  commercial  barium  chloride 
by  three  successive  crystallizations,  the  last  one  being  made  from  the  con- 
ductivity water.  The  salt  thus  obtained  was  analyzed. 

A  stock  solution  of  strontium  chloride  of  almost  the  maximum  satura- 
tion at  18°  was  made  from  a  special  grade  of  analyzed  chemicals.  The 
purity  of  the  strontium  chloride  in  this  concentrated  solution  was  tested 
by  precipitating  the  chloride  as  silver  chloride,  and  calculating  the  chloride 
found  in  terms  of  the  strontium  content.  The  chloride  analysis  was 
checked  by  an  independent  analysis  of  samples  of  the  same  solution  by 
precipitation  of  strontium  sulphate  from  an  aqueous  alcoholic  solution 
and  again  calculating  the  resulting  strontium  sulphate  as  strontium.  The 
mean  of  the  chloride  analyses  gave  a  strontium  content  of  33.820%,  and 
that  of  the  sulphate  analysis  33.740%,  an  actual  difference  of  .08%,  or  a 
precentage  difference  of  a  little  over  two-tenths  of  one  per  cent.  The 
strontium  chloride  was  further  tested  spectroscopically  and  found  to  be 
free  of  barium ;  even  sodium  was  present  apparently  in  minute  quantity. 

Analyzed  anhydrous  calcium  chloride  was  added  to  conductivity  water 
in  excess.  The  solution  was  filtered,  and  to  it,  was  added  a  slight  excess  of 
the  redistilled  hydrochloric  acid  sufficient  to  overcome  the  alkaline  reaction 
of  the  original  solution.  This  excess  of  hydrochloric  acid  was  eliminated 
by  adding  precipitated  calcium  carbonate  to  the  solution  and  passing  air 
through  the  boiling  solution  to  remove  carbon  dioxide  gas.  The  solution 
was  then  neutral.  Three  samples  of  the  calcium  chloride  solution  thus 
prepared  were  treated  with  silver  nitrate  and  from  the  weights  of  the 
silver  chloride,  the  calcium  content  was  calculated,  giving  4.163,  4.162  and 
4.161  per  cent,  an  average  value  of  4.162  per  cent.  Three  other  samples 
of  the  same  solution  were  evaporated  to  dryness  with  dilute  sulphuric  acid 
and  the  calcium  content  was  determined  from  the  weights  of  the  calcium 
sulphate,  the  values  being  4.152,  4.166  and  4.145  per  cent,  giving  an  aver- 
age value  of  4.154  per  cent.  The  difference  between  this  last  value  and  the 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCb,  SrCb  AND  Bad*       7 

average  value  for  the  calcium  content  by  the  chloride  method  is  0.008%,  or 
in  terms  of  the  mean  calcium  content,  4.158,  the  difference  is  a  little  less 
than  two-tenths  of  one  per  cent. 

b.  Apparatus. 

Measurements  of  this  type  have  been  made  by  numerous  investigations 
( Acree  Am.  Chem.  J.  46,  632,  1911 ;  Harned,  J.  A.  C.  S.  37,  2460,  1915 ; 
Ellis,  J.  A.  C.  S.  38,  737,  1916 ;  Lewis,  Brighton  &  Sebastian,  J.  A.  C.  S. 
39,  2245,  1917),  but  the  cells  employed  here  differed  in  some  respects  from 
any  previously  described.  One  type  of  cell  was  employed  for  the  meas- 
urement of  the  combination 

H2  I  MeCI2  (c)  in  HC1  (0.1)  |  HgCl  |  Hg 

It  was  an  H  shaped  cell  and  is  shown  in  Fig.  1. 


FIG.  1 


.8        THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCfe,  SrCb  AND  BaCL 

The  side  marked  C  is  the  calomel  electrode.  In  the  first  cells  contact 
011  the  calomel  electrode  side  was  made  through  a  glass  tube  fixed  in  a  one- 
hole  rubber  stopper  in  the  end  of  which  tube  was  sealed  a  platinum  wire 
similar  to  the  arrangement  shown  in  the  calomel  side,  C,  of  Fig.  2.  It 
sometimes  happened,  however,  that  when  the  rubber  stopper  holding  the 
glass  tubing  was  inserted  into  the  calomel  limb  of  the  cell,  air  pressure 
was  produced  in  the  calomel  chamber  above  the  solution.  When  the 
stopcock  S  was  subsequently  opened  for  a  measurement  a  certain  amount  of 
calomel,  lodged  between  the  points  A  and  S,  would  be  suddenly  carried 
through  to  the  hydrogen  electrode  side.  The  lead  wires  for  the  calomel 
electrode  were  therefore  thrust  into  mercury  in  the  small  side  tube  shown 
to  the  left  of  C  which,  in  turn,  was  in  contact  with  the  calomel  electrode 
through  a  platinum  wire  fused  into  the  bottom  of  the  cell.  The  stopcock 
shown  above  C  was  always  kept  open  until  the  rubber  stopper  in  which 
the  former  was  fixed  had  been  securely  inserted  into  the  top  of  the  tube. 
By  following  this  procedure  no  calomel  was  forced  into  the  hydrogen  com- 
partment. 

In  the  first  cells  used  the  connecting  tube  of  the  cell  AB,  Fig.  1,  was  a 
piece  of  straight  side  glass  tubing.  Frequently,  however,  air  bubbles  col- 
lected near  the  stopcock  S  and  very  persistently  remained  there.  By  re- 
placing the  straight  side  tubing  with  a  tubing  flared  at  either  side  of  the 
stopcock  S,  as  shown  by  AB,  Fig.  1,  any  bubbles  which  were  present  when 
the  cell  was  set  up  were  very  easily  removed. 

As  mentioned  later,  it  was  customary  to  shake  the  cell  until  its  elec- 
tromotive force  had  attained  a  constant  value.  This  shaking  invariably 
caused  some  calomel  to  lodge  even  in  the  flared  tube  between  the  points 
A  and  S  ajs  a  result  of  which,  if  the  stopcock  were  opened  for  some  time, 
a  certain  small  amount  of  calomel  might  be  carried  into  the  hydrogen 
electrode  chamber.  In  order  to  eliminate  this,  a  connecting  tube  of  the 
shape  indicated  by  A'  B'  was  tried.  A  certain  amount  of  calomel,  it  was 
observed,  still  lodged  near  the  stopcock  just  above  the  elbow  of  the  tube. 
Moreover,  at  the  same  point  in  the  tube  A'B'  a  bubble  would  collect  which 
was  difficult  to  dislodge.  Finally,  therefore,  a  connecting  tube  of  the  type 
shown  at  A"B"  was  used.  By  pouring  the  electrolyte  into  the  tube  first 
until  the  side  SB"  was  completely  filled,  and  then  adding  the  calomel,  the 
presence  of  air  bubbles  near  the  stopcock  was  entirely  avoided.  The  cal- 
omel here  used  had  previously  been  equiliberated  at  25°  with  a  solution  of 
the  particular  chloride  of  a  definite  concentration  for  several  days.  This 
arrangement  of  the  connecting  tube  A"B"  at  an  angle  of  about  45°  to  the 
limbs  of  the  cell  had  the  marked  advantage  that  no  calomel  would  lodge 
near  the  stopcock,  for  after  each  shaking  it  would  roll  to  the  bottom  of  the 
calomel  electrode  chamber. 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCL,  SrCfc  AND  BaCb       9* 

The  hydrogen  electrode  was  kept  always  completely  immersed  in  the 
electrolyte  and  placed  in  such  a  position  that  the  hydrogen  bubbles  coming 
from  the  equiliberating  chamber  M  would  be  divided  by  the  platinum  foil. 
The  hydrogen  electrode  chamber  was  provided  with  a  trap  T  permanently 
inserted  in  the  rubber  stopper  which  closed  the  tube.  By  having  the  end 
of  the  small  escape  tube  of  the  trap  under  the  surface  of  the  electrolyte  in 
the  bowl  of  the  trap,  the  space  above  the  surface  of  the  liquid  in  the 
hydrogen  electrode  chamber  was  kept  filled  with  hydrogen. 

The  hydrogen  was  first  passed  through  a  solution  of  the  electrolyte  in 
the  equiliberating  tube  M,  thereby  becoming  saturated  before  coming  into 
contact  with  the  solution  in  the  hydrogen  electrode  chamber,  and  thus 
preventing  any  evaporation  in  the  chamber.  It  has  been  determined  that 
equiliberating  tubes  of  the  above  type  (M  in  Figs.  1  &  2)  are  satisfactory 
for  saturating  the  hydrogen. 

After  each  measurement  the  hydrogen  electrode  was  removed,  any 
possibly  adhering  calomel  (indicated  by  a  gray  color  instead  of  the  intense 
black  of  the  platinum  sponge)  was  dissolved  by  immersing  the  electrode 
in  nitric  acid.  After  rinsing  with  distilled  water  the  electrode  was  recoated 
by  making  it  the  cathode  in  a  chlorplatinic  acid  solution,  from  twenty  to 
forty-five  minutes,  the  current  density  being  from  20  to  50  milli-amperes. 
H2  |  MeCl2  (c)  in  HC1  (0.1)  |  KCl(Sat.)  |  HgCl  |  Hg 

Fig.  2  represents  the  potassium  chloride  cell. 


FIG.  2 


10      THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCh,  SrCb  AND  BaCh 

Calomel  previously  equiliberated  for  several  days  with  a  solution  of 
potassium  chloride  saturated  at  25°  was  poured  into  the  calomel  chamber 
C  along  with  the  mercury.  The  bridge  RR  was  then  carefully  filled  with 
the  same  potassium  chloride  solution,  as  well  as  the  cup  P.  At  the  bottom 
of  the  cup  a  few  crystals  of  potassium  chloride  were  always  present.  The 
bulb  I/  was  likewise  filled  with  the  solution.  The  equiliberating  tube  M,  the 
hydrogen  electrode  chamber  II ,  the  bridge  R',  as  well  as  the  bulb  L,  were 
all  filled  with  a  solution  of  the  particular  electrolyte  being  measured,  that 
is  with  MeCl2  (c)  in  IIC1  (0.1).  This  electrolyte  filled  the  capillary 
tubing  Y  the  end  of  which  dipped  into  the  saturated  potassium  chloride 
solution  in  the  cup  P  when  a  measurement  was  being  made. 

When  no  measurements  were  being  taken,  a  cup,  really  a  short  test 
tube  of  heavy  glass  fitted  over  the  rubber  stopper  on  the  end  of  the  capil- 
lary Y  where  previously  the  cup  P  had  been.  By  means  of  this  device  the 
saturated  potassium  chloride  half  of  the  cell,  C  RP,  would  be  successively 
attached  to  any  number  of  half  cells,  YR'HM.  After  each  measurement 
the  solution  from  the  reservoir  bulb  Li  was  run  through  the  capillary  and 
the  potassium  chloride  carefully  removed  from  the  outside  surface  of  the 
capillary  tubing  by  bibulous  paper.  Similarly,  the  potassium  chloride  solu- 
tion was  renewed  by  opening  the  stopcock  below  the  bulb. 

The  hydrogen  was  generated  electrolytically  by  passing  the  current 
through  a  10%  solution  of  sodium  hydroxide.  A  current  of  about  two 
amperes  was  used.  A  20%  sodium  hydroxide  solution  was  first  tried  but 
this  attacked  the  electrodes.  Even  with  a  10%  solution  it  was  found  that 
copper  in  contact  anywhere  with  the  sodium  hydroxide  solution  was 
attacked.  Finally  a  platinum  anode  suspended  by  a  nickel  wire  and  a 
nickel  cathode  held  in  place  by  a  wire  of  the  same  material  were  used  in 
the  generator.  A  cell  thus  built  seemed  to  be  able  to  supply  hydrogen 
continuously  and  for  an  indefinitely  long'  time.  Finally,  the  glass  vessels 
which  contained  the  alkali  solution  were  attacked  to  some  extent.  In  order 
to  maintain  a  constantly  uniform  gas  pressure,  each  cell  was  provided 
with  its  own  hydrogen  generator.  During  the  greater  part  of  the  inves- 
tigation three  cells  were  being  measured  simultaneously ;  for  a  short  time 
four  cells  were  set  up. 

To  prevent  any  admixture  of  the  hydrogen  with  oxygen  the  tube  in 
which  the  anode  was  suspended  extended  almost  to  the  bottom  of  the  vessel 
containing  the  electrolyte.  The  electrolyte  was  forced  up  into  this  same 
tube  by  the  back  pressure  of  the  generated  hydrogen.  The  level  in  this 
tube  was  regulated  by  the  stopcock  attached  to  the  tube  M  (Figs.  1  &  2), 
and  was  maintained  at  such  a  height  that  the  hydrogen  bubbled  regularly 
and  continuously  through  the  hydrogen  electrode  compartment,  H.  Be- 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCk,  SrCb  AUD  BaCL*      11 

tween  the  hydrogen  generator  an^  the  cell  there  was  placed  first  in  the 
hydrogen  line  a  Dreschel  wash  bottle  containing  concentrated  sulphuric 
acid.  The  hydrogen  was  then  led  through  a  tower  containing  sticks  of 
fused  sodium  hydroxide,  after  which  it  entered  the  equiliberating  vessel 
M  The  electromotive  force  of  the  cells  was  measured  on  a  Wolff  poten- 
tiometer having  a  total  resistance  of  15,000  ohms.  A  null  point  was  ob- 
tained by  balancing  the  cell  against  two  large  Weston  cells  (Hulett — 
Physical  Review — 1909)  in  series.  Before  and  after  each  measurement  the 
latter  were  compared  with  a  standard  Weston  cell.  The  latter  in  turn  was 
occasionally  compared  with  a  new  Weston  certified  by  the  Bureau  of 
Standards  in  1921. 

Immediately  before  taking  a  set  of  readings  the  stopcocks  S,  Fig.  1,  on 
all  the  cells  were  opened,  the  large  Hulett  design  Weston  compared  with 
the  standard,  after  which  the  cells  were  read  in  rapid  succession.  Each 
cell  had  its  own  lead  wires  to  a  three  way  cup  switch  placed  beside  the  poten- 
tiometer. Finally  the  large  working  cells  were  rechecked  and  the  stop 
cocks  closed. 

The  temperature  of  the  bath  was  controlled,  to  within  -f.05°  by  means 
of  a  very  large  vessel  filled  with  toluene  whose  volume,  changing  with  the 
temperature,  moved  a  thin  mercury  column  in  immediate  contact  with  the 
toluene.  The  mercury  made  electrical  contact  with  a  platinum  wire  and 
thereby  opened  and  closed  the  electric  heating  circuit. 

c.  Measurements. 

All  of  the  electrolytic  solutions  were  made  up  on  the  basis  of  a  frac- 
tional or  multiple  part  of  a  mole  per  1000  grams  of  water.  The  amounts 
of  the  constituents  of  each  solution  were  determined  by  weight;  in  no 
single  instance  were  volumetric  methods  employed.  Temperature  coeffi- 
cients were  thereby  eliminated.  The  strengths  of  the  stock  solutions  of 
hydrochloric  acid,  calcium  chloride  and  strontium  chloride  were  determined 
by  precipitation  of  silver  chloride. 

For  weighing  substances  up  to  about  70  grams,  a  balance  with  a  sen- 
sitiveness of  two  ten  thousandths  of  a  gram  per  division  of  pointer  scale  was 
used ;  for  larger  quantities  a  beam  balance  with  a  sensitiveness  of  approxi- 
mately two  one  hundredths  of  a  gram  per  scale  division  was  available. 
The  stock  solution  of  redistilled  hydrochloric  acid  analyzed  for  its  acid  con- 
tent at  the  beginning  of  the  investigation  had  a  mean  value  of  7.3237% 
for  four  samples,  with  a  maximum  deviation  from  the  mean  for  any  one 
sample  of  0.0057%,  and  a  maximum  difference  for  any  two  samples  of 
0.010%.  Because  the  hydrochloric  acid  present  in  the  cells  was  the  most 


12      THERMODYNAMIC  PROPERTIES  OF  0.1  M  HCl  IN  CaCb,  SrCb  AND  BaCU 

important  constituent  of  the  electrolyte,  the  stock  solution  was  reanalyzed 
at  the  end  of  the  investigation  and  found  to  have  an  acid  content  of  7.3335% 
with  a  maximum  difference  of  0.0082%  and  a  maximum  deviation  of 
-{-.0051%.  The  change  had  been  negligible.  The  values  of  several  cells 
were  checked  with  solutions  having  the  slightly  different  acid  factor,  and 
found  to  be  practically  unchanged.  Two  samples  of  the  calcium  chloride 
solution  gave  a  mean  value  of  31.847%  content  with  a  difference  of  0.005%, 
and  two  analyses  of  the  strontium  chloride  solution  indicated  that  19.284% 
of  the  compound  was  present.  In  the  latter  analysis  the  difference  was 
0.024%.  It  might  be  noted  that  in  order  to  secure  concordant  results  of 
these  almost  saturated  salt  solutions,  it  was  found  necessary  to  wash  the 
precipitated  silver  chloride  at  teast  ten  times  with  acidulated  water. 

From  the  determination  of  the  concentration  as  described  above,  the 
molal  content  of  each  solution  was  obtained  by  dividing  the  strength  of 
the  solution  expressed  in  per  cent  by  the  molecular  weight  of  the  particular 
salt.  Since  it  was  necessary  to  know  the  weight  of  the  solution  containing 
one  molecular  weight  of  the  salt  the  molar  strength  as  found  above  was 
divided  into  the  per  cent  of  water  present  with  the  salt.  This  latter  num- 
ber was  obviously  obtained  by  subtracting  the  salt  concentration  expressed 
in  per  cent  from  one  hundred.  The  result  multiplied  by  a  hundred  an$ 
added  to  the  gram  molecular  weight  of  the  particular  chloride  gave  the 
total  weight  of  solution  per  mol.  of  salt.  For  fractional  molar  solutions, 
proportional  parts  of  this  number  were  taken. 

The  amount  of  water  to  be  added  was  easily  found  from  the  above 
calculation.  The  water  present  with  the  one-tenth  molal  hydrochloric  acid 
also  decreased  by  its  weight  the  water  necessary  to  make  the  one  thousand 
grams  present  with  the  salt.  In  the  barium  chloride  solutions  fractional 
parts  of  the  two  molecules  of  water  of  crystallization  were  regarded  as  a 
part  of  the  water  of  dilution. 

The  calomel  which  was  to  be  used  for  the  cells  was  shaken  at  least 
eight  times  with  separate  portions  of  the  particular  solution  after  which 
it  was  allowed  to  stand  in  the  thermostatic  bath  at  25°  for  some  hours 
before  using.  A  cell  did  not  attain  its  maximum  voltage  until  the  hydrogen 
electrode  had  been  exposed  to  the  stream  of  hydrogen  for  about  six  hours. 
Before  a  reading  was  taken  the  stopcock  S,  Fig.  1,  was  opened,  then  closed, 
and  the  cell  shaken.  After  the  calomel  had  settled  the  reading  of  the  electro- 
motive force  of  the  cell  was  checked.  This  procedure  was  continued  until 
the  cell  had  acquired  a  relatively  constant  voltage.  In  the  case  of  the 
concentrated  potassium  chloride  cells,  Fig.  2,  the  calomel  electrode  side  of 
which  was  attached  in  turn  to  each  salt-acid  hydrogen  electrode  half  as 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HCl  IN  CaCb,  SrCl*  AND  BaCI*     13 

previously  mentioned,  this  shaking  process  was  discontinued  after  a  con- 
stant and  correct  value  for  the  combination 

H2  |  HCl  (0.1)  |  KC1  (Sat.)  |  HgCl  |  Hg 

had  been  secured.  The  value  regarded  as  correct  was  that  obtained  by 
Fales  and  Vosbufgh  (loc.  cit.)  namely  0.3103.  The  value  here  found  as  a 
result  of  fifty  checked  and  separate  groups  of  readings  was  0.3100,  which 
is  practically  within  the  limit  of  error  as  given  by  the  investigators  referred 
to  above.  The  HCl  (0.1)  side  of  a  cell  wa!s  kept  in  the  bath  and  used  as 
a  check  on  the  elSectrojmotive  force  values  o|  the-  salt>-acid  cells. 

;       i       .'!'";:'  (    •  I 

After  the  double!  cell'  (Fig.  1)  had  attained  constant  value  at  25P  the 

temperature  of  the  thermostatic  bath  was  changed  to  either  18°  or  30°, 
the  stopcock  opened  and  the  voltage  read.  The  cell  was  then  shaken,  and,  if 
a  change  in  value  occurred,  repeatedly  shaken  until  constancy  was  obtained. 
Then  the  bath  was  brought  back  to  its  initial  temperature  and  the  cell 
again  tested.  The  differences  in  voltage  between  the  averages  of  the  values 
thus  obtained  were  used  for  the  determination  of  the  temperature  coeffi- 
cients. (Table  III.) 

The  mean  values  for  the  electromotive  force  readings  of  the  double 
cells  are  given  in  Table  I. 

TABLE  I. 

25°  VALUES  E.  M.  F.  DOUBLE  CELLS 

c  BaCl2  SrCl2  CaCl2 

0.00  0.39898  0.39898  0.39898 

0.10  0.37530  0.37500  0.37462 

0.20  0.36337  0.36318  0.36305 

0.30  0.35503  0.35449  0.35326 

0.50  0.34155  0.34031  0.33986 

0.75  0.32786  0.32630  0.32529 

1.00  0.31678  0.31471  0.31176 

1.3  0.30358  0.31280 

The  object  of  the  investigation  was  not  primarily  to  establish  the  elec- 
tromotive force  value  of  any  one  particular  strength  of  a  single  salt  but  to 
determine  the  relative  values  for  the  different  strengths  of  all  three  salts. 
Therefore,  at  first,  cells  of  different  solution  strengths  of  the  same  salt  were 
measured  and  the  results  plotted. 


14      THEBMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCb,  SrCb  AND  BaCh 


/SO 


'0££  C 


FIG.  3 

Where  the  values  were  obviously  incorrect  in  comparison  with  neigh- 
boring points  on  the  graph  of  the  same  salt  or  of  the  other  two  salts,  new 
cells  of  that  strength  were  placed  in  the  bath  and  kept  there  until  the  value 
of  the  electromotive  force  was  established  beyond  doubt.  Thus  it  followed 
that  certain  cells  were  read  but  a  few  times  while  the  mean  value  for 
others  was  the  result  of  numerous  sets  of  readings.  The  value  of  the  l.M 
strontium  chloride  cell  is  the  mean  of  more  than  fifty  readings,  the  l.M 
calcium  chloride  of  over  twenty  readings  and  that  of  the  three-fourths 
strontium  chloride  of  some  forty  readings ;  no  cell  was  read  less  than  four 
times  at  each  temperature. 

It  is  thus  evident  that  the  control  of  the  work  depended  upon  the 
graphs,  Figs.  3  &  4.  While  some  of  the  values  depicted  upon  the  graphs 
are  the  results  of  less  than  a  dozen  readings,  it  should  be  noted  that  neigh- 
boring points  on  the  same  smooth  line  are  established  by  many  readings. 
These  latter  values  may  therefore  be  regarded  as  control  points  or  control 
values.  One  cell  only  of  each  kind  was  set  up  in  the  bath  at  any  one  time. 
The  mean  values  in  Table  I  are  therefore  dependent  upon  readings  taken 
on  different  days.  It  should  be  added  that  all  the  cells  except  those  noted 
below  were  read  over  a  period  of  at  least  three  days  and  frequently  a  week. 
The  values  for  the  one-tenth  molal  strength  of  the  double  cells  are  the  only 
ones  which  depend  upon  one  day 's  readings.  It  is  apparent  that  the  values 
obtained  represent  readings  which  were  made  at  different  times  over  a 
considerable  period  and  should  therefore  be  easily  reproducible. 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCh,  SrCb  AND  BaCb      15 

The  variation  in  the  e.  m.  L  values  of  ten  of  the  cells  amounted  to 
approximately  one-tenth  of  a  millivolt.  In  six,  the  variation  ranged  from 
two-tenths  to  five-tenths.  In  the  case  of  the  three-tenths  barium  chloride 
and  of  seventy-five  hundredths  calcium  chloride  the  values  given  in  Table  I 
are  each  the  result  of  two  sets  of  independent  readings  which  varied  by  one 
millivolt  but  these  values  are  the  only  ones  of  the  kind  in  the  table.  It 
is  believed  that  the  cells  were  reproducible  to  within  ±  0.2  of  a  millivolt. 


The  values  found  for  the  temperature  coefficients  are  given  in  Table 


III. 


TABLE  III. 


AE 
AT 


BaCl2 
25°-ll8°   ;         30-25 


DOUBLE    CELLS 

SrCl2 
25-18 '         '  30-25 


CaCl2 
25-18  36-25 


.1 

.2 
.3 
.5 
.75 
1.00 
1.3 

+0.000125     +0.000098 
+0.000092     +0.000069 
+0.000064     +0.000044 
+0.000018     +0.000000 
-0.000028     -0.000046 
-0.000070     -0.000089 
-0.000120     -0.000140 

+0.000108     +0.000083 
+0.000062     +0.000044 
I   +0,000027     +0.000012 
-0.000025     -0.000040 
-0.000076     -0.000095 
-0.000120     -0.000146 

+0.000098  :  +0.000070 
+0.000049     +0.000019 
+0.000010     -0.000020 
-0.000053     -0.000082 
-0.000117     -0.000145 
-0.000172     -0.000200 

These  values  were  obtained  by  plotting  the  differences  in  voltage  at  18°, 
25°  and  30°  and  continuing  the  measurements  until  acceptably  constant 
results  were  obtained.  In  certain  cells,  notably  the  calcium  cells,  the  var- 
iation was  remarkably  small,  in  fact  so  little  as  0.003  millivolt.  In  other 
cells  the  variation  was  larger.  It  is  believed  that  the  temperature  coeffi- 
cients are  reproducible  to  within  zt  0.005  millivolt. 

TABLE  II. 


E.  M.  JF'S.  FOR  CON.   KCl  CELLS— 25° 


0.1 

0.2 

0.3 

0.5 

0.75 

1.00 

1.30 


BaCl2 

0.00140 
0.00301 
0.00480 
0.00882 
0.01432 
0.01989 
0.02658 


SrCl2 

0.00160 
0.00337 
0.00530 
0.00959 
0.01531 
0.02141 


CaCl, 

0.00194 
0.00390 
0.00599 
0.01041 
0.01641 
0.02310 


16      THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCh,  SrCb  AND  BaCl* 

The  voltage  values  for  the  half  cells  (Fig.  2),  subtracted  from  the 
HC1 — no  salt  value  mentioned  above  (0.3100),  are  given  in  Table  II,  and 
are  plotted  in  Fig.  4. 


F  'IG.  4. 


ff?ATE 
ClLO#/t 


f  Cr, 


00O8       ffO/O       00'? 


FIG.  4 


The  electromotive  force  readings  were  corrected  for  partial  hydrogen 
pressure  by  direct  reading  of  the  correction  from  graphs  showing  varia- 
tion of  voltage  with  barometric  pressure  for  each  one  of  the  three  temper- 
atures at  which  measurements  were  made.  The  values  for  the  e.  m.  f. 
indicated  on  the  chart  were  derived  from  the  expression  (Harned — loc.  cit.) 


„     RT 
E  =  —  In 


760 


PP-PH.O 

It  should  be  stated  that  considerably  more  difficulty  was  experienced 
in  measuring  the  concentrated  electrolytes  than  with  the  more  dilute,  both 
in  establishing  electromotive  force  values  and  in  determining  temperature 
coefficients.  It  is  here  suggested  that  this  difficulty  was  possibly  caused  by 
an  appreciable  solubility  of  the  calomel  electrode  in  the  concentrated  solu- 
tions of  the  salts  under  consideration. 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  OaCb,  SrCh  AND  Bad*      17 


III.   (a)   THE    FREE    ENERGY  AND   HEAT   CONTENT 
INCREMENTS  OF  THE  CELL  REACTION.  • 


The  decrease  in  free  energy  resulting  from  the  reaction  in  the  cell  of 

2  HgCl+H2  =  2  Hg+2  HC1  (0.1M) 

has  been  computed  from  the  values  for  the  electromotive  force  given  in 
table  IV  for  18°,  25°  and  30°  by  multiplying  each  value  there  given  by 
2  x  96500. 

TABLE  IV. 


c 

Bad, 
0.00 
0.1 
0.2 
0.3 
0.5 
0.75 
1.00 
1.3 


0.39785 
0.37443 
0.36273 
0.35458 
0.34142 
0.32806 
0.31727 
0.30442 


E2B 

0.39898 
0.37530 
0.36337 
0.35503 
0.34155 
0.32786 
0.31678 
0.30358 


0.39963 
0.37579 
0.36372 
0.35525 
0.34155 
0.32762 
0.31633 
0.30288 


SrCI2 

0.1 

0.2 

0.3 

0.5 

0.75 

1.00 


0.37424 
0.36265 
0.35429 
0.34049 
0.32683 
0.31555 


0.37500 
0.36318 
0.35449 
0.34031 
0.32630 
0.31471 


0.37544 
0.36340 
0.35455 
0.34011 
6.32581 
0.31398 


CaCl, 

0.1 

0.2 

0.3 

0.5 

0.75 

1.00 


0.37393 
0.36271 
0.35319 
0.34022 
0.32612 
0.31296 


0.37462 
0.36305 
0.35326 
0.33986 
0.32529 
0.31176 


0.37497 
0.36315 
0.35316 
0.33929 
0.32456 
0.31076 


18      THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCb,  SrCb  AND  BaCb 

The  decrease  in  free  energy  thus  determined  for  18,  25  and  30  degrees 
is  given  for  each  concentration  of  the  salts  in  Table  V,  columns  2,  3  and 
4. 


BaCl2 

0.00 

0.10 

0.20 

0.30 

0.50 

0.75 

1.00 

1.3 

SrCl2 

0.1 

0.2 

0.3 

0.5 

0.75 

1.00 

CaCl2 

0.1 

0.2 

0.3 

0.5 

0.75 

1.00 


(-AF), 


76785. 
72265. 
70007. 
68434. 
65894. 
63316. 
61233. 
58753. 


72228. 
69991. 
68378. 
65715. 
63078. 
60901. 


72168. 
70003. 
68166. 
65662. 
62941. 
60401. 


TABLE  V. 

(-AF)25      (-AF)30 


AF 
AT 


C-AH)« 


77003. 
72433. 
70130. 
68521. 
65919. 
63277. 
61139. 
58591. 


72375. 
70094. 
68417. 
65680. 
62976. 
60739. 


72302. 
70069. 
68179. 
65593. 
62781. 
60170. 


77129. 
72527. 
70198. 
68563. 
65919. 
63231. 
61052. 
58456. 


72460. 
70136. 
68428. 
65641. 
62881. 
60598. 


72369. 
70088. 
68160. 
65483. 
62640. 
59977. 


+29.0 
+ 21.00 
+  14.50 
+  9.50 
+  1.30 
-  7.00 
-15.50 
-25.00 


+  19.00 
+  10.80 
+  4.03 
-  6.40 
-17.50 
-27.50 


+  15.00 
+  5.02 
-  2.30 
- 14.00 
-25.50 
-35.50 


68361. 
66175. 
65809. 
65690. 
65474. 
65363. 
65758. 
66041. 


66713. 
66935. 
67225. 
67557. 
68191. 
68934. 


67832. 
68579. 
68864. 
69646. 
70386. 
70749. 


In  determining  the  heat  content  function   (  —  AH)  column  five,  table 
V,  the  expression 


(-AH)  =  (-AF)-Td 


(-AF) 
dT 


was  used.  But  it  was  found  at  least  to  be  impracticable  if  not  impossible 
to  express  AF)  as  a  function  of  T  and  subsequently  to  differentiate  the 
equivalent  expression 

d(AF)          AH 
dt  "  T2 

and  from  this  differentiated  expression  to  calculate  the  numerical  value 
of  (_AH).  For  it  was  evident  that  AF==f(T)  varied  markedly  for  various 
concentrations  of  the  three  different  salts.  The  values  for 

-AF  } 


Td 


dT 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCb,  SrCb  AND  BaCh     19 

were  therefore  determined  by,  a  graphic  method.  The  values  of 
the  free  energy  decreases  as  given  in  columns  2,  3  and  4,  Table  V, 
were  plotted  against  their  respective  temperatures  and  a  smooth  curve 
was  drawn  through  the  three  points  thus  determined.  The  scales  used  for 
plotting  differed  for  the  various  groups  of  free  energy  values.  In  general, 
when  the  variation  of  free  energy  with  the  temperature  was  slight,  a  large 
scale  was  employed.  Thus,  in  the  case  of  five-tenths  barium  chloride  and 
of  three-tenths  calcium  chloride  a  scale  of  five-tenths  of  a  centimeter  per 
joule  and  of  2  centimeters  per  degree  was  used.  For  most  of  the  concen- 
trations, however,  a  scale  of  one-tenth  or  of  one-fifth  of  a  centimeter  per 
joule  and  of  1  centimeter  per  degree  was  found  to  be  satisfactory.  The 
increase  or  decrease  in  energy  for  one-half  of  a  degree  on  either  side  of 
the  25°  value  was  scaled  off  on  the  curve.  The  values  thus  obtained  are 
given  in  column  five,  Table  V. 

In  order  to  check  the  values  for 


column  five,  Table  V,  each  one  of  these  values  was  plotted  against  the 
corresponding  salt  concentration.  All  of  these  points  should  exactly  deter- 
mine a  curve  which  should  be  perfectly  smooth  and  give  no  evidence  of 
discontinuities.  All  points  were  directly  on  such  curves  except  those  for 
five-tenths  barium  chloride  and  three-tenths  calcium  chloride;  values  for 
these  concentrations  given  in  column  5,  Table  V,  were  scaled  from  the 
last  mentioned  curves.  These  values  did  not  lie  directly  on  their  respective 
curves  because  it  is  evident  from  their  free  energy  values  for  18°,  25° 
and  30°,  Table  V,  that  each  has  a  maximum  free  energy  value  between 
18°  and  25°  which  value  could  not  be  determined  unless  the  temperature 
coefficients  for  that  particular  temperature  were  known. 

* -p 

By  multiplying  each  one  of  these  values  for  by  the  value  of 

AT 

T  (=298°)  and  subtracting  the  result  from  the  corresponding  value  for 
the  free  energy  at  25°,  Table  V,  columns  2,  3  and  4,  the  values  in  joules 
of  the  change  in  heat  content  function  are  determined.  They  are  tabulated 
in  column  five,  Table  V. 


20     THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCb,  SrCb  AND  BaCb 


b.  THE   FREE   ENERGY   AND   HEAT    CONTENT   DECREASE   OP 

TRANSFER  OF  2  MOLS.  OF  HC1  FROM  MeCl2  (0)  IN  HC1 

(0.1M)  to  HCL   (0.1M). 


The  free  energy  and  heat  content  function  of  the  transfer  of  two  gram 
ions  of  hydrogen  and  chlorine  are  given  in  Table  VI. 

TABLE  VI. 

c            18°            25°  30°  (-AH)26 
BaCl2 

0.1            4520.            4570.  4602.  2186. 

0.2           6778.            6873.  6931.  2552. 

0.3            8351.            8482.  8566.  2671. 

0.5           10891.           11084.  11210.  2887. 

0.75          13469.           13726.  13898.  2998. 

1.00          15552.           15864.  16077.  2603. 

1.3           18032.           18402.  18673.  2320. 
SrCl2 

0.1            4557.            4628.  4669.  1648. 

0.2           6794.            6909.  6993.  1426. 

0.3           8407.           8586.  8701.  1136. 

0.5          11070.           11323.  11488.  804. 

0.75          13707.           14027.  14248.  170. 

1.00          15884.           16264.  16531.  -573. 


0.1  4617.  4701.  4763.  529. 

0.2  6782.  6934.  7041.  -218. 

0.3  8619.  8824.  8969.  -503. 

0.5  10923.  11410.  11646.  -1285. 

0.75  13844.  14212.  14489.  -2025. 

1.00  16384.  16833.  17152.  -2388. 

They  were  obtained  by  subtracting  the  values  for  the  decrease  in  free 
energy  for  each  salt  concentration  (Table  V)  from  the  value  for  the  free 
energy  given  at  the  top  of  Table  V,  at  salt  concentration  0.00.  In  a  similar 
manner  the  heat  content  function  values  were  obtained  from  Table  V  and 
are  given  for  25°  in  the  last  column  of  Table  VI. 

c.  INDEPENDENT  ACTIVITIES  OF  IONS. 

Maclnnes  (loc.  cit.)  first  clearly  pointed  out  that  in  solutions  of 
different  electrolytes  having  a  common  ion,  the  latter  may  have  the  same 
activity  independent  of  the  accompanying  ions.  In  particular  the  ratio  of 


THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCh,  SrCb  AND  BaCb      21 

the  activity  of  the  chloride  ion  in  a  given  concentration  of  the  latter  to  a 
constant  concentration  of  the  same  ion  should  be  identical  for  barium, 
strontium  and  calcium  chlorides.  The  data  obtained  in  this  investigation 
affords  further  proof  of  this  theory.  (Earned,  J.  A.  C.  S.,  43,  1814, 
1920.) 

Mathematically  the  above  mentioned  ratio  may  be  obtained  by  using 
equations  (8)  and  (9)  of  this  paper.  If  (9)  is  subtracted  from  (8)  we 
have 


that  is, 


-  F[E0(2)  -  E(2)l  =  RTl 


_  [Eo(2)  -  E(2)]  = 


11"" 


aH(0.1)     aC(0.1) 


aH(0.1) 


which  reduces  finally  to 


*         aH(0.1)  aCl(0.1) 


aH(0.1) 


-  [E0(2)  -  E(2)] 


aCl(0.1) 


Values  for  E0(l)  —  E(l)  can  be  readily  obtained  from  Table  I  by 
subtracting  the  values  for  each  concentration  of  the  three  chlorides  from 
the  electromotive  force  value  given  at  the  head  of  the  table  as  concen- 
tration 0.00.  These  values  are  given  in  the  first  part  of  Table  VII. 


TABLE  VII. 


c 

0.1 
0.2 
0.3 
0.5 
0*75 
1.00 
1.3 

01 

0.2 

03 

05 

075 

1.00 

1.3 


BaCl2 
0.02368 
0.03561 
0.04395 
0.05743 
0.07112 
0.08220 
0.09540 


0.02228 
0.03260 
0.03915 
0.04861 
0.05680 
0.06231 
0.06882 


SrCl2 
0.02398 
0.03580 
0.04449 
0.05867 
0.07268 
0.08427 


0.02238 
0.03243 
0.03919 
0.04908 
0.05737 
0.06286 


CaCl2 
0.02436 
0.03593 
0.04572 
0.05912 
0.07379 
0.08618 


0.02242 
0.03203 
0.03973 
0.04871 
0.05728 
0.06308 


The  values  for  E0(2)-E(2)  are  those  given  in  Table  II.  The  dif- 
ference between  these  two  sets  of  values  is  shown  in  the  second  part  of  Table 
VII.  The  maximum  difference  for  any  one  concentration  is  0.00058  volts 
and  the  average  difference  for  the  six  concentrations  given  is  but  .00041  of 


22      THERMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  CaCk,  SrCk  AND  BaCk 

a  volt.  This  is  very  small  considering  the  high  concentrations  of  the  solu- 
tions. The  slight  deviation  still  further  substantiates  the  belief  that  com- 
mon ion  activities  under  the  same  conditions  are  identical.  Harned  in  his 
work  with  the  alkaline  metal  chlorides  (loc.  cit.)  likewise  found  that  the 
deviation  present  was  well  within  the  probable  experimental  errors. 


d.  THE  CALCULATION  OP  THE  ACTIVITY  COEFFICIENTS  OF 
THE  HYDROGEN  ION  AND  THE  CHLORINE  ION  AT  25°  IN  0.1M 
HYDROCHLORIC  ACID  CONTAINING  BARIUM,  STRONTIUM  AND 
CALCIUM  CHLORIDES  AT  CONCENTRATIONS  UP  TO  1.  M. 


As  shown  above  under  the  reaction  of  Independent  Activities  of  Ions 
[Bo(D  -  E(l)l  -  [E0(2)  -  E(2)]  =  5 


a  Cl(O.l) 

The  values  in  volts  for  the  first  member  of  the  above  equation  are 
given  in  the  second  part  of  Table  VII.  The  value  for  aCi(0.i)  has  been  de- 
termined by  Harned  (J.  A.  C.  S.,  44,  252,  1922),  and  calculated  as  .0779. 
From  the  same  source  the  value  for  aH  is  derived  as  0.0868.  Substituting 
numerical  values  in  the  above  equation  and  solving  for  acl  there  is  given 

log  ac.  =  log  .0779 +— 

.05915  RT 

where  the  constant  .05915  represents  the  numerical  values  of  —  x 
logarithmic  conversion  factor. 

In  a  similar  manner  the  expression  for  an    is 
log  aH  =  .og. 07638+^ 

The  values  of  e.  m.  f.  for  acl  were  obtained  from  the  first  part  of 
Table  VI  and  those  for  an  from  Table  II.  The  values  for  aci  and  aH 
as  calculated  above  are  given  in  Table  VIII. 

TABLE  VIII.     PART  1. 


Values  of 

c  BaCl2  SrCl2  CaCl2 

0.1  0.18544  0.18617  0.18645 

0.2  0.27712  0.27530  0.27105 

0.3  0.35760  0.35817  0.35746 

0.5  0.51684  0.52638  0.51883 

0.75  0.71090  0.72684  0.72414 

1.00  0.88097  0.90003  0.90790 

1.3  1.13508 


THEBMODYNAMIC  PROPERTIES  OF  0.1  M  HC1  IN  OaCl»,  SrCb  AND  BaCh     23 

TABLE  VIII.     PART  2. 

Values  of  (EH) 

c                                       Bad,                                       SrCl2  CaCl2 

0.000                                  0.0868                                       0.0868  0.0868 

0.100                                  0.0969                                       0.0974  00987 

0.200                                  0.1029                                       0.1042  0.1064 

0-300                                  0.1102                                       0.1127  01151 

0.500                                  0.1290                                       0.1332  01371 

0.750                                  0.1599                                       0.1661  0.1735 

1-000       e                         0.1984                                      0.2105  0.2248 
1.3                                   0.2577 


SUMMARY. 

1.  Measurements  of  the  electromotive  forces  of  the  cells 

H2  I  MeCl2  (c)  in  HC1  (0.1)  |  HgCl  |  Hg 

at  18°,  25°  and  30°  containing  barium,  strontium  and  calcium  chlorides, 
have  been  made. 

2.  Measurements  of  the  cells 

H2  |  MeCl2  (c)  in  HC1  (0.1)  |  KC1  (Sat.)  |  HgCl  |  Hg 

at  25°  containing  barium,  strontium  and  calcium  chlorides,  nave  also  been 
made, 

3.  Values  for  the  cells 

H2  |  HC1  (0.1)  |  HgCl  |  Hg 
and  H2  |  HC1  (0.1)  |  KC1  (Sat.)  |  HgCl  |  Hg 

at  25°  were  checked  with  values  of  the  same  cells  found  by  other  investi- 
gators. 

4.  The  values  for  the  free  energies  and  heat  content  decreases  of  the 
cell  reaction 

H2f  2  HgCl  =  2HCl  (0.1)+2Hg 

in  the  presence  of  barium,  strontium  and  calcium  chlorides,  respectively, 
have  been  computed. 

5.  The  decrease  in  free  energy  and  heat  content  function  of  transfer 
of  the  chlorine  and  hydrogen  ions  respectively  from    MeCl2     (c)  in  HC1 
(0.  1M)  to  HC1  (0.1)  have  been  compiled. 

6.  The  independent  chloride  ion  activity  in  the  various  salt  solutions 
proposed  by  Maclnnes  and  found  to  hold  within  narrow  limits  by  Harned, 
has  been  further  substantiated. 

7.  The  activities  of  the  hydrogen  ion  and  the  chlorine  ion  at  25°  in 
0.1M  hydrochloric  acid  containing  barium,  strontium  and  calcium  chlorides 
at  concentrations  up  to  l.M  have  been  found. 


< -ay lord  Uros. 

Makers 

Syracuse,  N.  Y. 
PAT.  JAN,  21,  1908 


494210 


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